The product two numbers is 36. The sum of the numbers is 13. What are the two numbers.

Let's call the two numbers "x" and "y". We know that their product is 36, so we can write: xy = 36 We also know that their sum is 13, so we can write: x + y = 13 We can use the second equation to solve for one of the variables in terms of the other. For example, we can solve for y in terms of x: y = 13 - x Now we can substitute this expression for y into the first equation: xy = 36 x(13 - x) = 36 Expanding the left side, we get: 13x - x^2 = 36 Rearranging terms, we get a quadratic equation: x^2 - 13x + 36 = 0 We can solve this equation by factoring: (x - 4)(x - 9) = 0 So the solutions are x = 4 and x = 9. If we plug each of these values into the equation y = 13 - x, we get: y = 13 - 4 = 9 y = 13 - 9 = 4 So the two numbers are either 4 and 9 (in some order).